基于表征分形维数的结构面产状分组效果评价方法及应用

doi:10.13722/j.cnki.jrme.2017.1632

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摘要进行结构面产状分布特征的分形描述时，传统分形维数同时受到产状样本数和样本自身分布特征的影响，考虑到传统方法的不足，提出表征分形维数的概念。引入蒙特卡洛法生成服从Fisher分布的不同离散程度的样本，对结构面产状分形维数随样本数的变化趋势进行分析得出，分布曲线总体呈“三段式”分布，即分形维数曲线增长先较快，后变慢，最终趋于平稳；取分形维数增长速率第一次出现减小对应的样本数为最优样本数，并以最优样本数对应分形维数作为表征分形维数对样本产状分布特征进行描述。结合一实际矿山边坡工程，引入聚类算法对结构面产状进行分组，将表征分形维数与传统有效性指标的分组效果进行比较，结果表明，表征分形维数不用预先假设产状样本的分布形式，能很好地反映结构面实际的分布特征。

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	李立辰1
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	杨松1
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	姚赵田1
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关键词 ：岩石力学, 结构面产状, 蒙特卡洛法, 表征分形维数, Fisher分布, 聚类算法

Abstract：The traditional fractal dimension describing the characteristics of discontinuity orientation is influenced by both the joint number and the characteristics of discontinuity orientations. The definition of representative fractal dimension is proposed to overcome the limitations of traditional methods. Monte Carlo method is introduced to generate the discontinuity samples that conform to the Fisher distribution and to represent different dispersion levels. The analysis of the fractal dimension with changing sample size reveals that there is a“three-level”trend generally，i.e.，the fractal dimension increasing fast at first，then slowly and finally reaching almost stable. The joint number at the increasing rate of fractal dimension slowing down for the first time is defined as the optimal joint number，and the corresponding fractal dimension is defined as the representative fractal dimension. The clustering method is introduced to group the joint data in a mining slope project. Comparison between the clustering results of representative fractal method and traditional validity index indicates that the fractal dimension does not require a pre-defined distribution form for joint sample and can describe the characteristics of discontinuity orientation better.

Key words： rock mechanics discontinuity orientation Monte Carlo method representative fractal dimension Fisher distribution clustering method

引用本文:

李立辰1，2，吴文兵1，2，3，4，杨松1，2，姚赵田1，2. 基于表征分形维数的结构面产状分组效果评价方法及应用[J]. 岩石力学与工程学报, 2018, 37(7): 1641-1648.
LI Lichen1，2，WU Wenbing1，2，3，4，YANG Song1，2，YAO Zhaotian1，2. An evaluation method of clustering results of discontinuity orientation #br# based on the representative fractal dimension and its application. , 2018, 37(7): 1641-1648.

链接本文:

http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2017.1632 或 http://www.rockmech.org/CN/Y2018/V37/I7/1641

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